let a, 6, b, 24 be a G.P find a and b

a,6,b,24 are in GP. To determine a and
b:

Since the terms are in GP, the successive terms should
have common ratio. So

 6/a = b/6 =
24/b.

From the last pair, b/6 = 24/b we get: b^2 = 24*6
=144.

So b = sqrt(144) = 12or
-12.

Therefore r = 24/12 = 2. or 24/-12 =
-2.

From the first pair, 36 = ab Or 36 = a*12. So a = 36/12
= 3.

Or  so a =3 or -3. and b = 12 or -12 Therefore the
series is

3 , 6, 12 , 24.
Or

-3 , 6 , -12 , 24 , if r = -2.